Which of the below given gate(s) cannot be used for implementing combinational circuits?
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Which of the below given gate(s) cannot be used for implementing combinational circuits?
- I) NAND
- II) NOR
- III) EXOR
Show answer & explanation
NAND, NOR, and EXOR gates are all universal logic gates or functionally complete gates that can be used to implement any combinational circuit. NAND and NOR are individually universal (can implement AND, OR, NOT), while EXOR combined with other basic gates can implement any combinational logic. All three gates are valid building blocks for combinational circuits.
Step-by-step Derivation:
Analysis of each gate:
NAND Gate: Universal gate. Can implement:
- NOT: A NAND A = NOT A
- AND: (A NAND B) NAND (A NAND B) = A AND B
- OR: (A NAND A) NAND (B NAND B) = A OR B
→ Can implement any combinational circuit
NOR Gate: Universal gate. Can implement:
- NOT: A NOR A = NOT A
- OR: (A NOR B) NOR (A NOR B) = A OR B
- AND: (A NOR A) NOR (B NOR B) = A AND B
→ Can implement any combinational circuit
EXOR Gate: Functionally complete with constants. Can implement:
- Basic XOR functionality for parity and comparison
- When combined with other gates or constants, can implement any combinational circuit
- Commonly used in arithmetic circuits (adders, subtractors)
→ Can implement combinational circuits
Conclusion: All three gates CAN be used for implementing combinational circuits. The correct answer is B.